Simple groups, generation and probabilistic methods

Tim Burness

Simple groups, generation and probabilistic methods

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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Abstract

It is well known that every finite simple group can be generated by two elements and this leads naturally to a wide range of problems that have been the focus of intensive research in recent years, such as random generation, (2,3)-generation and so on. In this talk I will discuss some recent progress on similar problems for subgroups of simple groups, with applications to primitive permutation groups and the study of subgroup growth (this is joint work with Liebeck and Shalev). I will also recall the notion of the spread of a finite group and I will explain how probabilistic methods (based on fixed point ratio estimates for simple groups) have been used to shed light on a far reaching conjecture of Breuer, Guralnick and Kantor. Time permitting, I will finish by mentioning some related problems on the generating graph of a finite group.

Original language	English
Title of host publication	Groups St Andrews 2017 in Birmingham, 5th-13th August 2017
Subtitle of host publication	London Mathematical Society Lecture Note Series
Publisher	Cambridge University Press
Number of pages	30
Volume	455
ISBN (Print)	9781108728744
Publication status	Published - 1 Apr 2019

Publication series

Name	London Mathematical Society Lecture Note Series
Publisher	Cambridge University Press
ISSN (Print)	0076-0552

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This is the accepted author manuscript (AAM). The final published version (version of record) will be available online via Cambridge University Press at https://www.cambridge.org/gb/academic/subjects/mathematics/algebra/groups-st-andrews-2017-birmingham?format=PB. Please refer to any applicable terms of use of the publisher.
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Cite this

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Simple groups, generation and probabilistic methods. / Burness, Tim.

Groups St Andrews 2017 in Birmingham, 5th-13th August 2017: London Mathematical Society Lecture Note Series. Vol. 455 Cambridge University Press, 2019. (London Mathematical Society Lecture Note Series).

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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Simple groups, generation and probabilistic methods

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